Top Student at Their Peak-Chapter 232 - 108: The Future Qiao Yu-Qiao Xi’s Upper Bound Theorem!_6

Chapter 232: Chapter 108: The Future Qiao Yu-Qiao Xi’s Upper Bound Theorem!_6

But after three deep breaths, he calmed himself down, then picked up his phone and decided to send a WeChat message to his teacher.

"Mr. Chen, please help me find a few more papers on the upper bound estimate problem of rational points on curves and Peter Schultz’s papers."

The reply came quickly: "What do you need these papers for?"

"I want to see just how difficult this stuff really is."

"Professor Schultz is currently focused on solving the Langlands Conjecture. Honestly, reading his papers now is just a waste of time without any real significance."

"It’s okay, Mr. Chen, I just want to get a rough understanding; it won’t waste too much time."

"Alright, I’ll send them to your email in an hour."

Yu Wei put down his phone with a serious expression. freeweɓnovēl.coɱ

He was feeling a bit defiant, to the point where he was too restless to concentrate on his problem-solving.

Lately, he had been intensely practicing various problems for the Olympic Competition, preparing to redeem himself in the first special training session, but who would have thought that Qiao Yu, who went to Yanbei University, had already started doing research projects.

And it seemed like that guy was serious about his research.

Because the first special training was actually held at Yanbei University.

He really didn’t want Qiao Yu to keep showing off in front of him, but Yu Wei knew very well that to surpass Qiao Yu, he first had to at least understand the gap between them.

Luckily, he didn’t have to wait long before there was a notification from his email on his phone.

Instead of logging in on his phone, Yu Wei logged into his email directly on his computer and Coach Chen had downloaded three papers for him.

Two were about deriving the upper bound for rational points on curves, and the other was Peter Schultz’s "Perfectoid Spaces: A survey". The email specifically noted that this was the easiest paper by Peter Schultz to understand.

Yu Wei downloaded Schultz’s paper first.

After all, Mr. Chen had said that reading Schultz’s papers at this time was a waste of time, and he was still feeling a bit defiant.

But after opening and reading it, he fell silent, and even the dissatisfaction in his heart diminished significantly.

Yu Wei prided himself on having a certain foundation in algebraic geometry, and he had heard of Peter Schultz’s name. He believed he might not fully understand the paper, but at least he would know what it was talking about.

But after reading through the overview, he realized that his understanding of these frontier mathematical researches seemed to have some misconceptions.

This wasn’t something you could understand just by knowing a bit of college-level advanced mathematics.

Were they not the same age? Had the gap really grown to this extent?

He didn’t want to believe this was true, but every time Qiao Yu mentioned something that sounded like bragging, he later found out it was true. Not just once, but three or four times... to the point where he no longer trusted his own judgement.

Thinking about that, Yu Wei suddenly felt a bit uneasy; unconsciously, both his hands had clenched into fists...

It’s unavoidable; people always underestimate the pain until they actually get hit...

...

In Star City, Qiao Xi was sitting at the desk Qiao Yu used to use for writing, calmly working on a problem set.

The winter sun of Star City was just right, shedding through the window onto her body, though it didn’t bring much warmth, it felt very comfortable.

But what made Qiao Xi feel most comfortable was looking at those familiar yet strange textbooks, working on these familiar yet strange exercises, it seemed to take her back to the age when she held endless expectations for the future.

Going to college in Beijing...

"Ring..." The sudden ringing of the phone brought Qiao Xi out of her dazed state...

She spaced out again. Looking at the math paper she had already half-done in front of her, Qiao Xi lazily turned her head to glance at the phone, it was another call from that brat at home.

She swiped the screen and chose to answer on speakerphone.

"Hello, what’s up?"

"Mom, what are you doing?"

"Doing the math papers you sent back."

"Oh, are they hard?"

"They seem a bit different from what we learned back then, but they’re manageable. A bit challenging to do, but not particularly difficult."

"Well, that’s normal, the curriculum changes. Ask me any questions you have, this is a special treatment only you get to enjoy."

"Enough chatter, why did you call?"

"Ah, Mom, I seem to have run into a problem. It’s one of those damned math propositions, I’ve been thinking hard but still can’t figure out how to solve it. What do I do? Both my teacher and elder teacher have high hopes for me, and I’m already hitting a bottleneck just as I’ve begun."

"Oh? A very difficult proposition?"

"I don’t think it’s very difficult. Actually, I’ve already solved it, but the result is particularly complicated with a bunch of parameters. I want to simplify the result, push all the complexities into the proof process, but I’ve tried everything and still can’t handle it."

"Then why not ask your advisor? Why call me when I can’t help you solve it?"

"I asked Old Xue, but Old Xue suggested avoiding the most complex processes, which would render it meaningless."

"Oh, is it possible that your result is actually a false proposition?"

"Impossible! I have this feeling, you know intuition? I’m sure there’s a way to simplify the result and form a theorem, but I just don’t know how to start."

"So you’re calling for comfort? Hurry up and say, ’please, mom, comfort me.’

Qiao Xi put down the pen in her hand, stretched out her fair hand to place the phone in front of her, and then propped her cheek with one hand, ready to hear her bratty son complain.

An unusual experience, as Qiao Yu rarely showed this kind of helpless attitude in front of her.

The only pity was, she seemed unable to help.

"Don’t tease me, Mom, I’m bothered enough..."

"Oh, alright then, tell me why your result has so many parameters?"

"Because the problem is controlled by multiple geometric constraints, each geometric tool used comes with a different set of limitations. These tools must be used to condense the results into a formula."

"Oh..." Qiao Xi began to ponder, then asked, "Are all the tools indispensable?"

"Yes, I’ve already tried reducing the constraints or improving the tools, but it didn’t work."

"So there’s no commonality at all in the constraint conditions of these tools?"

"Commonality?"

"Yes, since each tool must be used, and each tool has different constraints, to simplify, you must find commonality, or say, connections between these conditions."

"Hmm? Mom, what you’re saying makes some sense."

"So you can try to study whether there’s any potential connection between those different parameters, if there is, maybe you can unify multiple parameters? Isn’t solving math problems about finding possible logical connections between different conditions?"

Qiao Xi said offhandedly, feeling that Qiao Yu should understand this better than she did...

But the other side was silent for a while...

"Hey, why aren’t you saying anything?" Qiao Xi felt a bit puzzled.

"Mom, did you let that man win so he could rank first?"

"Hmm?"

"I’ve been busy thinking about optimizing those tools to control parameters, why didn’t it occur to me that since they can’t be controlled, why not unify these parameters instead? Thank you, Mom, I think I found a direction!"

"Really? Are you serious?"

"Of course! Gosh, I’ve always envied those mathematicians for their ability to freely create tools. What I’m doing now is creating tools too, but why did I forget when I was focusing too hard that one can solve it by creating tools even without ready-made ones?!

Thank you, Mom! By the way, if your suggestion really helps me solve this issue, this theorem from now on will be called the Qiao Yu-Qiao Xi Upper Bound Theorem! And you’ll be the second author of this paper!"

With that, he hung up the call before Qiao Xi could say anything.

Qiao Xi shook her head inexplicably...

That brat, what’s wrong with him? Why would she want to be the second author?! And the Qiao Yu-Qiao Xi Upper Bound Theorem? What on earth is that!